Lagrangian Floer theory over integers: spherically positive symplectic manifolds

Abstract

In this paper we study the Lagrangian Floer theory over $\mathbb{Z}$ or ${\mathbb{Z}}_2$. Under an appropriate assumption on ambient symplectic manifold, we show that the whole story of Lagrangian Floer theory in \cite{fooo-book} can be developed over ${\mathbb{Z}}_2$ coefficients, and over $\mathbb{Z}$ coefficients when Lagrangian submanifolds are relatively spin. The main technical tools used for the construction are the notion of the sheaf of groups, and stratification and compatibility of the normal cones applied to the Kuranishi structure of the moduli space of pseudo-holomorphic discs.

68 pages; 4 figures; v2) 72 pages, to appearin the special issue of Pure and Applied Mathematics Quarterly dedicated to Denis Sullivan's 70th birthday

References in corpus (2)

• Cyclic symmetry and adic convergence in LagrangianFloer theory
• Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle

Cited by in corpus (1)

• Technical details on Kuranishi structure and virtual fundamental chain